Bottom Line:
We present a pseudospectral method application for solving the hyperchaotic complex systems.In this new application, the MSRM is used to solve famous hyperchaotic complex systems such as hyperchaotic complex Lorenz system and the complex permanent magnet synchronous motor.We compare this approach to the Runge-Kutta based ode45 solver to show that the MSRM gives accurate results.

ABSTRACTWe present a pseudospectral method application for solving the hyperchaotic complex systems. The proposed method, called the multistage spectral relaxation method (MSRM) is based on a technique of extending Gauss-Seidel type relaxation ideas to systems of nonlinear differential equations and using the Chebyshev pseudospectral methods to solve the resulting system on a sequence of multiple intervals. In this new application, the MSRM is used to solve famous hyperchaotic complex systems such as hyperchaotic complex Lorenz system and the complex permanent magnet synchronous motor. We compare this approach to the Runge-Kutta based ode45 solver to show that the MSRM gives accurate results.

fig8: Comparison between the MSRM and ode45 results for the complex permanent magnet synchronous motor.

Mentions:
The results obtained were compared to those from the MATLAB inbuilt solver, ode45. The ode45 solver integrates a system of ordinary differential equations using explicit 4th and 5th Runge-Kutta formula. Tables 3 and 4 show a comparison of the solutions of the complex permanent magnet synchronous motor computed by the MSRM and ode45. In Figures 6, 7, and 8, the MSRM graphical results are also compared with ode45 and good agreement is observed. The MRSM phase portraits in Figures 9 and 10 were also found to be exactly the same as those computed using ode45. This shows that the proposed MSRM is a valid tool for solving the complex permanent magnet synchronous motor.

fig8: Comparison between the MSRM and ode45 results for the complex permanent magnet synchronous motor.

Mentions:
The results obtained were compared to those from the MATLAB inbuilt solver, ode45. The ode45 solver integrates a system of ordinary differential equations using explicit 4th and 5th Runge-Kutta formula. Tables 3 and 4 show a comparison of the solutions of the complex permanent magnet synchronous motor computed by the MSRM and ode45. In Figures 6, 7, and 8, the MSRM graphical results are also compared with ode45 and good agreement is observed. The MRSM phase portraits in Figures 9 and 10 were also found to be exactly the same as those computed using ode45. This shows that the proposed MSRM is a valid tool for solving the complex permanent magnet synchronous motor.

Bottom Line:
We present a pseudospectral method application for solving the hyperchaotic complex systems.In this new application, the MSRM is used to solve famous hyperchaotic complex systems such as hyperchaotic complex Lorenz system and the complex permanent magnet synchronous motor.We compare this approach to the Runge-Kutta based ode45 solver to show that the MSRM gives accurate results.

ABSTRACTWe present a pseudospectral method application for solving the hyperchaotic complex systems. The proposed method, called the multistage spectral relaxation method (MSRM) is based on a technique of extending Gauss-Seidel type relaxation ideas to systems of nonlinear differential equations and using the Chebyshev pseudospectral methods to solve the resulting system on a sequence of multiple intervals. In this new application, the MSRM is used to solve famous hyperchaotic complex systems such as hyperchaotic complex Lorenz system and the complex permanent magnet synchronous motor. We compare this approach to the Runge-Kutta based ode45 solver to show that the MSRM gives accurate results.